The present invention generally relates to a digital picture multiplication device and a digital picture multiplication method, and particularly, to a device and a method for a single- and/or multi-dimensional even and/or biased extension, magnification, contraction and/or deformation (hereafter collectively "universal multiplication" or simply "multiplication") of a binary or multi-value digital picture, or in other words, a universal conversion in number and/or arrangement of pixels in a digital picture, permitting a compositional context of an original image to be substantially held.
1. Description of the Related Art
Recent years have observed an increasing need for a multiplication of a digital picture in a variety of fields such as of a digital copier, facsimile, printer, recorder, editor, monitor, projector, television, virtual image processor, etc. (hereafter collectively "digital image processor").
In fields of an analog picture, a multiplication is a typical technique that one can do by knowledge of a projection and/or interpolation, in which a continuous variation of an image is promised.
In contrast, in a digital picture, any image is composed of a set of pixels individually allowed to have one of a limited number of discrete states of representation, such as a black and a white. Still less, no pixel in a picture can be deformed or divided.
However, there were several pioneers in the digital field also. They made their own ways, developing their methods for a digital picture multiplication. As one of most successful developments, there was a multiplication method consistent with an intuitive projection concept. As still advancing now, the multiplication method is well known as a dot density conversion method relatively high of a picture quality. Each dot corresponds to a pixel.
FIGS. 1A to 1C are illustrations for describing a principle of the projection concept.
In FIG. 1A, according to the projection concept, an original or input picture PI is projected, by rays R of light from an imaginary point light source LS, onto an output picture format PF.sub.1 (broken line) to have a multiplied picture PM.sub.1 (solid line) mapped thereon as an ideal target picture to be imitated in an image data processing of the input picture PI to obtain an output picture PO.
The input picture PI is formatted, e.g., to a matrix of 5A.times.5B pixels, where A and B are positive integers. The output picture format PF.sub.1 comprises, e.g., a matrix of 4C.times.4D pixels, where C and D are positive integers. In the case of FIG. 1A, 5A=4C and 5B=4D so that the multiplied picture PM.sub.1 just overlaps the picture format PF.sub.1 and hence the output picture PO represents the same region as the input picture PI.
In a case of 5A&lt;4C and 5B=4D, as shown in FIG. 1B, a multiplied picture PM.sub.2 overlaps part of an output picture format PF.sub.2 so that a rectangular peripheral region .quadrature.EFGH is left, as it is blank, and hence an output picture represents an entire region of an input picture PI and a rectangular blank region which may be displayed in black.
In a case of 5A=4C and 5B&gt;4D, as shown in FIG. 1C, a multiplied picture PM.sub.3 covers, with part thereof, an entire region of an output picture format PF.sub.3 and has a rectangular peripheral region .quadrature.IJKL thereof exceeding the format PF.sub.3, so that an output picture represents part of an input picture PI.
The density conversion method employs an algorithm to determine a density relationship for a direct conversion from a two-dimensional subset of pixels of an input picture to a two-dimensional subset of pixels of a multiplied picture in consistency with the projection concept.
The algorithm is simplified, assuming that the conversion is made between binary values.
The simplification is based on a geometrical mode conversion which has been introduced by a Technical Report of the Institute of Electronics and Communication Engineers of Japan, Vol. 75, No. 147, IE75-November, 1975, pp. 37-44.
The geometrical mode conversion classifies into a number of pattern modes a set of geometrical relationships between a respective one of pixels of a picture to be output and a number of pixels vicinal thereto in an input picture, to have a distribution of the modes determined to be stored in a form of a conversion table, before using the table for a conversion of pixel-matrix size from the input picture to the output picture.
FIG. 2 shows a diagram of a 5.times.5 pixel matrix of a left-upper portion of an input picture overlapping a 4.times.4 pixel matrix of a left-upper portion of an output picture, for describing the geometrical mode conversion,
An input picture P100 comprises a set {x.sub.ab } of digital image data x.sub.ab formatted for a 5A.times.5B matrix of imaginary pixels Px(a,b) defined by solid lines in FIG. 2, where A and B are positive integers, and "a" and "b" are arbitrary integers such that 1.ltoreq.a.ltoreq.5A and 1&lt;b5B, respectively.
The input picture P100 is multiplied by a fraction of 16/25 so that an output picture P200 is composed of a set {y.sub.cd } of digital image data y.sub.cd formatted for a 4C.times.4D matrix of imaginary pixels Py(c,d) defined by broken lines in FIG. 2, where C and D are positive integers such that 4C=5A and 4D=5D, respectively, and "c" and "d" are arbitrary integers such that 1.ltoreq.c.ltoreq.4C and 1.ltoreq.d.ltoreq.4D, respectively.
When the input and output pictures P100 and P200 are monitored by an unshown input monitor and an unshown output monitor, respectively, if a display of the output monitor has the same size as a display of the input monitor, a respective one of 4C.times.4D actual pixels of the output monitor should display an image segment that is substantially identical in sense of vision to a combination of image segments displayed by those of 5A.times.5B actual pixels of the input monitor which partially or wholly overlap the above-mentioned respective pixel of the output monitor, as the display of the output monitor is supposed to be standing just in front of or behind that of the input monitor.
To be adaptive to such the requirement, among the image data Y.sub.cd of the output picture P200, that one Y.sub.cd (c=c.sub.0,d=d.sub.0), which is assigned to an arbitrary one Py(c.sub.0,d.sub.0) of the imaginary pixels Py(c,d), has a digital value thereof determined in accordance with a normalized value of a weighted sum .SIGMA.f(a,b).multidot.X.sub.ab ! of image data X.sub.ab of those imaginary pixels Px(a,b) of the input picture P100 which partially or wholly overlap the above-mentioned arbitrary pixel Py(c.sub.0,d.sub.0) of the output picture P200 when projected, where the suffix "0" collectively represents one or more particular integers in concern within an arbitrary defined range of integers, and "f(a,b)" (hereafter sometimes simply ("f") is a weighting factor of a corresponding pixel Px(a,b).
The weighting factor f(a,b) is proportional to an area by which the corresponding pixel Px(a,b) in the input picture P100 overlaps a concerned pixel Py(c.sub.0,d.sub.0) of the output picture P200.
For example, in a region of a first-row, first-column pixel Py(c.sub.0,d.sub.0) (c.sub.0 =1,d.sub.0 =1) of the output picture P200, there are four pixels Px(a,b) (a=1.about.2,b=1.about.2) of the input picture P100 overlapping therewith, wholly or in part, with an area ratio of 16:4:4:1. The four pixels Px(1,1), Px(1,2), Px(2,1) and Px(2,2) have their binary data values x.sub.11, x.sub.12, x.sub.21 and x.sub.22 and weighting factors f(1,1) (=16), f(1,2) (=4), f(2,1) (=4) and f(2,2) (=1). Accordingly, a weighted sum .SIGMA.fx.sub.ab ! of them is calculated such that: EQU .SIGMA.fx.sub.ab !=16x.sub.11 +4x.sub.12 +4x.sub.21 +1x.sub.22.
The weighted sum .SIGMA.fx.sub.ab ! is then divided by a sum Sf (=.SIGMA.f=16+4+4+1=25) of the weighting factors f to determine a normalized value, which is digitized by using a threshold value to provide a binary data value y.sub.11 for the pixel Py(1, 1) of the output picture P200.
Likewise, a data value y.sub.cd is calculated for each pixel Py(c, d) of the output picture P200. In the case of FIG. 2, such calculations amount to 16 patterns in total.
In any pattern of such calculation, an associated combination of weighting factors f(a,b) as well as a sum Sf of them can be predetermined, as a particular factor (=16/25) of the picture multiplication is provided, allowing an area ratio to be geometrically determined.
Therefore, a necessary number of combinations of conversion factors fc=f(a,b)/Sf are calculated in advance, and stored in a matrix form as a conversion table for use in a geometrical mode dot-density conversion from an input picture to an output picture, which may employ a logical expression such as for a pixel assignment and/or a pattern repetition.
It is unavoidable for the conventional method to use a conversion table to permit a picture multiplication to be processed at a practical speed.
Therefore, the conventional method can simply serve for an order-made picture multiplication in which a multiplication factor is fixed, in addition to that a memory with a significant capacity is necessary for storing a conversion table and that a significant man-hour is needed to provide for the conversion table.
Moreover, the conventional method can simply serve for a two-dimensional even multiplication in which an output picture coincides with an input picture in respect of a frame form, to use an entire region of the output picture for displaying an entire region of the input picture.
In other words, it is difficult for the conventional method to be flexibly adaptive to a single-dimensional multiplication or extension in which a frame of an output picture does not coincide with a frame of an input picture, or to any multi-dimensional multiplication other than a two-dimensional.
Further, it is hard for the conventional method to execute a biassed or deforming picture multiplication in which an equi-density is not guaranteed, whatsoever.
Such various restrictions in application of the conventional method seems owing to a conventional projection concept in which a single shot develops a final target picture and in which a better imitation to the target picture guarantees a better quality.
The present inventor thought the digital process should inherently be stepwise for a better flexibility; the digital image should inherently be a limited number of bits unable to be fully responsible for an excessive duty.
The present invention has been achieved with these points in mind.